There was an event to get shaymin, but it has ended so your chance is that someone trade it with you.
You can trade with someone who has Shaymin, but that's your only option. To get Shaymin, you need Oak's Letter or Action Replay.
No you cannot
The only way to get Shaymin in Pokémon Platinum without an Action Replay as of August 15, 2013 is by arranging a trade with another player that would have Shaymin and would be willing to trade it to you.
=Its not possible but getting aceus is without action replay=
you need walk through walls
Thats impossible
nintendo event and i know you are angry
oh that's easy you don't.
you cant
Only from event
There is only one way to get shaymin without the use of an action replay, and that is to go to a game store on a day where they give away free pokemon... at least that's how i got my shaymin without using my action replay. I went to Toys R Us and this dude was giving away free shaymin. I really can't say much more, but other than what i just told you, i don't think there is any other way to get a shaymin without an action replay. Sorry...
The only way to get Shaymin in Platinum without cheating or an event is through trading it with a friend.